Block Diagram Representation (Direct Form II (or called Canonic direct Form) xn yIn W(2)H2(2) ∠ X(=) ∑ hH(=)=∑ k=0 W(2)e MEN
17 Block Diagram Representation (Direct Form II) + z −1 z −1 + z −1 + b0 b1 bN−1 bN x[n] + z −1 z −1 + z −1 + a1 aN−1 aN y[n] w[n-1] w[n-2] w[n-N] w[n] Assume M = N = − = M k k k H z b z 0 1 ( ) = − − = N k k k a z H z 1 2 1 1 ( ) (or called Canonic direct Form) ( ) ( ) Y z W z = ( ( ) ) X W z z =
Block Diagram Representation (Direct Form II) 叫n2=∑awn-k+xn k=1 1小=∑bmn-kl k=0 xX wIn n wIn- H2(x) W(=) 1∑+x(()=2S==a k=0 W( k=1 b In-N 19
19 + z −1 z −1 + z −1 + b0 b1 bN−1 bN x[n] + z −1 z −1 + z −1 + a1 aN−1 aN y[n] w[n-1] w[n-2] w[n-N] w[n] Assume M = N Block Diagram Representation (Direct Form II) 1 0 ( ) ( ) ( ) M k k k W z Y z H z b z− = = = 2 1 1 ( ) ( ) ( ) 1 N k k k H z X z a W z z − = = = − 0 [ ] [ ] = = − M k k y n b w n k 1 [ ] [ ] [ ] N k k w n a w n k x n = = − +
Block Diagram Representation (Direct Form If Implementing Implementing poles zeros xIn ④→yln wIn- M ∑b H(=)=H2(=)H1(=)= k )a,k八(k=0 ∑a-k k=1 20
20 Block Diagram Representation (Direct Form II) + z −1 z −1 + z −1 + b0 b1 bN−1 bN x[n] + z −1 z −1 + z −1 + a1 aN−1 aN y[n] w[n-1] w[n-2] w[n-N] w[n] Assume M = N = − = M k k k H z b z 0 1 ( ) = − − = N k k k a z H z 1 2 1 1 ( ) 0 2 1 0 1 1 1 ( ) ( ) ( ) 1 1 M k M k k k N N k k k k k k k k b z H z H z H z b z a z a z − − = − − = = = = = = − − Implementing zeros Implementing poles
Block Diagram Representation (Direct Form In) How many Adders? N+M How many multipliers?N+M+1 How many delays? N+M xn wn 'n ∠ wIn- 2 n Assume M=N wIn-NI 21
21 Block Diagram Representation (Direct Form II) How many Adders? How many multipliers? How many delays? + z −1 z −1 + z −1 + b0 b1 bN−1 bN x[n] + z −1 z −1 + z −1 + a1 aN−1 aN y[n] w[n-1] w[n-2] w[n-N] w[n] Assume M = N N N N+M +M +M+1
Block Diagram Representation (Canonic Direct Form or direct Form In How many Adders? N+M How many multipliers? N+M+1 How many delays? max(M, N) X 0 N-1 Assume 1 MEN 22
22 Block Diagram Representation (Canonic Direct Form or direct Form II) How many Adders? How many multipliers? How many delays? max(M, N) + + + b0 b1 bN−1 bN x[n] + z −1 z −1 + z −1 + a1 aN−1 aN y[n] Assume M = N N N +M +M+1 N